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Question

1. Determine the equivalent resistance of the circuit shown in the figure. (Figure 1). Express your answer to three significant figures and include the appropriate units.

2. Determine the voltage across 820 ? resistor. Express your answer to two significant figures and include the appropriate units.

3. Determine the voltage across 960 ? resistor. Express your answer to two significant figures and include the appropriate units.

4. Determine the voltage across 680 ? resistor. Express your answer to two significant figures and include the appropriate units.

Answer “Determine the equivalent resistance of the circuit shown in the figure”.

Resistor Network:

For an electrical circuit of resistors, the total current in the circuit is found by calculating the equivalent resistance, and applying Ohm’s law. Further, the distribution of current takes place in such a way that the series resistors gets the same current, while parallel resistors get the same voltage.

Answer and Explanation:

We are given:

• An electrical circuit of three resistors with a battery:
  R₁ = 960Ω R₂ = 820Ω R₃ = 680Ω
• Battery Voltage, V = 12.0 V

(1) Equivalent resistance (Req) of the given circuit

Equivalent resistance (R₂₃) of R₂ and R₃

• Both R₂ and R₃ are in parallel, their equivalent is calculated as:
• 1/R₂₃ = 1/R₂+1/R₃
• 1/R₂₃ = 1/820+1/680
• R₂₃ = 371.7 Ω

Equivalent Resistance (Req) of R₁ and R₂₃

• Both R₁ and R₂₃ are in series, their equivalent is calculated as:
• Req = R₁+R₂₃
• Req = 960+371.7=1331.7 Ω

(2) Voltage (V₂) across resistor R₂ = 820 Ω

The total current in the circuit is calculated using ohm’s law as:

• I = V/Req = 12/1331.7 = 0.009 A

Therefore, voltage across R2 is calculated as:

• V₂ = I × R₂₃
• V₂ = 0.009×371.7 = 3.35 V

(3) Voltage (V1) across resistor R₁ = 960 Ω

Applying Ohm’s Law for resistor R₁

• V₁ = I × R₁
• V₁ = 0.009 × 960 = 8.64 V

(4) Voltage (V₃) across resistor R₃ = 680 Ω

Because the resistors R ₂ and R ₃ are in parallel , they both have the same voltage:

• V₃ =V₂ =3.35 V

Last words

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